Skip to content
Marlbridge

AP® Calculus AB · Unit 5 · Topic 5.10

Introduction to Optimization Problems: Topic Checklist (Calculus AB 5.10)

Specific “I can…” statements for setting up and solving optimization problems, each tied to the guide section and practice question that shows whether you can do it.

Work through the list without notes or a calculator. If you cannot do a statement, follow its link, then come back. Guide = study guide; Practice = practice questions. This topic is shared by Calculus AB and Calculus BC.

Understanding

  • I can explain why the search for a maximum or minimum inside an interval starts with critical points. (Guide: “What an optimization problem is”)
  • I can name the quantity to optimise, the constraint and the interval in a problem, whatever its setting. (Guide: “The common structure”; Practice Q2)
  • I can tell the maximum value apart from the location of the maximum, and answer the one that is asked. (Guide: “A note on notation and words”; Practice Q1, Q3)

Skills

  • I can use a constraint to write a quantity as a function of one variable. (Guide: Worked example 2; Practice Q3, Q6(a))
  • I can state the interval of allowed values from the situation, such as positive lengths. (Guide: “Where the interval comes from”; Practice Q2, Q6(a))
  • I can find the absolute maximum and minimum on a closed interval with the candidates test, including endpoints. (Guide: Worked example 1; Practice Q1, Q5)
  • I can find and test the critical point of a function I have built, then give the value and the dimensions that produce it. (Guide: Worked example 2; Practice Q6(b), Q6(c))
  • I can minimise a distance by working with its square. (Practice Q7(a)–(c))

Reasoning

  • I can justify an absolute extremum on an open interval with the single-critical-point argument and a first or second derivative test. (Guide: “The method”, step 7; Practice Q4, Q6(b))
  • I can explain why the second derivative test alone does not prove an absolute extremum. (Guide: “Common misconceptions”; Practice Q5 note)
  • I can explain why a critical point that seems natural may be a maximum when a minimum is wanted. (Practice Q7(d))

All ticked? Move on to Topic 5.11, Solving Optimization Problems, or return to the Calculus AB roadmap or the Calculus BC roadmap.

AP® and Advanced Placement® are trademarks registered by the College Board, which is not affiliated with, and does not endorse, this website. Marlbridge is an independent tuition provider. It is not an authorized AP course provider, an AP school or an exam centre, and these resources are not official College Board materials. Reading them or doing simulations does not meet the laboratory requirement of an AP science course.